Answers and Explanations 241
Answers
301–400
327.
−
+
( ) +
( )
1
2
3 2
1 2
1 2
x
g x
x
x g x
'
Begin by simplifying the given expression:
f x
xg x
x
x
x g x
( )
( )
( )
=
+
=
+
−
2
2
1 2
1 2
Then apply the product rule to the second term and the power rule to the first term:
= −
(
) +
+
= −
+
+
−
−
x
x g x x g x
x
g x
x
x g
( )
( )
( )
( )
(
2 1
2
1
2
1
2
3 2
1 2
1 2
3 2
1 2
1 2
x x )
x
f '
'
'
328.
− +






+
−






2
2
1
2
3
2
2
2
x
x
x
x
x
x
tan
s ec
Rewrite the original expression:
f x
x
x
x
x
x
x
( )
(tan )
( tan )
=
−






=
−
(
)
−
−
1 2
2
2
2
1
Then apply the product rule to get the derivative:
= −
+
(
)
+
−
(
)(
)
= − +






−
−
−
−
x
x
x x
x
x
x
x
tan
s ec
tan
2
2
2
2 2
3
2
2
1
2
3
2
x x
x
x
x
+
−






1 2
2
2
sec
x
( )
f '
329.
−
+
+
1 4
3
2
2
5 3
2 3
x
x
x
x
x
cos
sin
First simplify the given function:
f x
x
x x
x
x
x
x
x x
x
x
x
x
x
( )
cos
cos
cos
= −
=
−
=
−
−
−
2
2
2
3
2
2
3
2
1
23
Then apply the product rule to find the derivative:
= −
− −
+
−
)
(
= −
+
+
−
−
−
x
x
x
x
x
x
x
x
x
cos
( sin )
cos
sin
2
5 3
2 3
2
5 3
4
3
2
1 4
3
2
x x
2 3
x
( )
f '